Solve the next problem graphically (Please become neat). Draw the polytope on the x-y coordinate system (can performed either manually , or computer). Show every intersection in the polytope and identify the idea (x, sumado a coordinate) the place that the objective function is maximized and provide that value.
Improve Z sama dengan 3, one particular + 2, 2 Susceptible to: 1, 1 + 1, 2? 10 8, you + 1, 2? 24 and x1, x2? 0 Solution: Stage (a) may be the origin (0, 0) wherever Z(a) sama dengan 3*0 & 2*0 sama dengan 0Point (b) is the intersection of range 2 and X-axis (3, 0) in which Z(b) = 3*3 + 2*0 = 9 Stage (c) is a intersection of line 1 and range 2 (2, 8) in which Z(c) sama dengan 3*2 & 2*8=22. (Optimum Solution) Stage (d) is the intersection of line you and Y-axis (0, 10) where Z(d) = 3*0 + 2*10 = 20 Y Times d a b c I 2 Problem a few. (30 Points) Work through the simplex technique (in algebraic form) step-by-step to solve the following problem.
Show most work and provide the alternatives for each varying at every version of the simplex. Maximize z . = 4, 1 & 3, 2 + 4, 3 Be subject to: 2, 1 + 2, 2 & 1, three or more? 20 2, 1 & 1, 2 + 2, 3? 13 1, you + 1, 2 & 3, several? 15 and x1, x2, x3? 0 Solution: Issue 6. (30 Points) The Weigelt Company has three branch plants with surplus production ability. Fortunately, the organization has a cool product ready to begin production, and three plant life have this capability, so a number of the excess capability can be used this way. This product may be made in three sizes, significant, medium, and small, that yield a net unit profit of $420, $360, and three hundred, respectively. Crops 1, 2, and 3 have the excessive capacity to generate 750, nine hundred, and 400 units every day of this product, respectively, whatever the size or perhaps combination of sizes involved. The quantity of available in-process storage space also imposes a limitation within the production rates of the cool product.
Plant life 1, 2, and 3 have 13, 000, 12, 000, and 5, 1000 square feet, correspondingly, of in-process storage space readily available for a day’s production with this product. Every unit of the large, channel, and small sizes produced every day requires twenty, 15, and 12 square feet, respectively. Product sales forecasts suggest that in the event available, nine hundred, 1, two hundred, and 750 units in the large, method, and modest amounts, respectively, would be sold each day. At each herb, some employees will need to be laid off unless almost all of the plant’s excessive production capability can be used to develop the new item. To avoid layoffs if possible, administration has decided that the vegetation should make use of the same percentage of their excessive capacity to develop the new item. Management would like to know how much of each from the sizes should be produced by each one of the plants to increase profit. 1 .
Come up with a geradlinig programming model for this trouble by: A. Listing and labeling all of the decision factors. B. Creating an objective function for the model. C. List each of the constraints pertaining to the model. I want an entire model, not merely an Exceed sheet.
2 . Solve the model using Excel solver or perhaps Open Office Solver. Give the value for every decision adjustable and the goal function.